The success of the ambitious programme of the upcoming Run III at the LHC and its subsequent
High-Luminosity upgrade [1]}, [2]} relies on achieving the highest possible
accuracy not only in the experimental measurements
but also in the corresponding
theoretical predictions.
A key component of the latter are the
parton distribution functions (PDFs),
which parametrize the quark and gluon
substructure of the colliding protons [3]}, [4]}.
PDFs are dictated by non-perturbative QCD dynamics
and hence must be phenomenologically extracted by matching a wide range
of experimental data with the corresponding
theoretical predictions.
The determination of PDFs and their uncertainties requires a robust statistical
framework which minimises unnecessary assumptions while implementing known
theoretical constraints such as QCD evolution, sum rules, positivity, and
integrability.
